Higher June 2018 Paper 3 Q22

AQACurrent spec1 markCircle Theorems

22 \(A\), \(B\) and \(C\) are points on a circle.

\(DCB\) is a straight line.

\(PAQ\) is a tangent to the circle.

Circle through A, B and C. DCB is a straight line with D outside the circle; angle m is the angle DCA. PAQ is a tangent at A, and angle BAQ is 56 degrees

Not drawn accurately

Sam is trying to work out the size of angle \(m\).

Here is his working.

angle \(ACB\) = 56°angles in the same segment are equal
\(m\) = 180° − 56°angles at a point on a straight line add up to 180°
\(m\) = 124°

Make a criticism of his working. [1 mark]